Is a "Blender Game Engine" game built into native code or something higher level like python?
The binary that executes the game (i.e. Blenderplayer) is native code compiled from a combination of C and C++. I don't think there are any Python based Blender operators that run when you play a game. So yes it's completely 'native'.

If you choose to extend the game with Python script, which will be interpreted at runtime with a Python 3.3 (as of Blender 2.70) interpreter, then it will be a mix of 'native' component and interpreted scripts.

Unless you are doing some serious Python coding, the performance overhead of Python is very small.